Finite Group Databasebeta

← #14299986

Subgroups — #14299986

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2#11751029C211yesmaximal, characteristic, complemented
3C2×#90990C211yesmaximal, characteristic, complemented
4C2×#90965C211yesmaximal, characteristic
5C2×#90965C211yesmaximal, characteristic
6C5×#4524C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10599463—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C2×C3×C42×C5C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×#6712—21no—
15C22×C5×C3⋊C8C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C3×C4×D20—22no—
20C3×C4×D20—22no—
21#91115—21no—
22#90990—22no—
23#90965—22no—
24#90965C414yescomplemented
25#71606—51nomaximal, Hall
26C2×C4×D20D311yescharacteristic
27C2×#3953—31no—
28C2×#3953—31no—
29C2×#3950—31no—
30#65217—31no—
31C5×#336—31no—
32#64771—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C22×Dic15—21no—
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×D20D412yes—
45C2×C3×D20Q812yes—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15C2×C412yescomplemented
55#6712—42no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C2×C5×C3⋊C8C2×C412yescomplemented
62C3×#685—24no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5D412yes—
65C2×C3×C4×D4—51no—
66C2×#832—51no—
67C2×#832—51no—
68C2×#807—51no—
69#4928—51no—
70#4529—51no—
71#4524D511yescharacteristic, complemented
72C22×D20C2×D311yescharacteristic
73C22×C4×D5—21no—
74C22×C5×C8—31no—
75C22×C5×C8—31no—
76C2×C42×C5C2×D311yescharacteristic
77C2×#685—21no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5C2×D311yescharacteristic
81C2×#683—61no—
82C4×D20—22no—
83C4×D20—22no—
84#3963—61no—
85#3953—34no—
86#3953—62no—
87#3950—62no—
88#1862—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—22no—
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5D812yes—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C4⋊C414yescomplemented
122C3×C4×D5—48no—
123C5×C3⋊C8—22no—
124C5×C3⋊C8—41no—
125C22×C3×D4—51no—
126C23×C3×C4—101no—
127C3×C4×D4—102no—
128C3×C4×D4—102no—
129C2×C3×C4⋊C4—51no—
130C2×C3×C22⋊C4—101no—
131C2×C3×C42C2×D511yescharacteristic
132C2×C4⋊Dic3—51no—
133C2×C4⋊Dic3—51no—
134C2×Dic3⋊C4—101no—
135C22×C3⋊C8C2×D511yescharacteristic
136C22×C3⋊C8C2×D511yescharacteristic
137#832—54no—
138#832—102no—
139C3⋊#95—101no—
140#807—102no—
141C23×D5—21no—
142C22×C4×C5#6711yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—61no—
147C22×Dic5—61no—
148C2×D20—21no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20Dic612yes—
152C2×D20C4×D312yes—
153C2×D20#6712yes—
154C2×C4×D5—24no—
155C2×C4×D5—42no—
156C2×C4×D5—42no—
157C2×C5×C8—32no—
158C2×C5×C8—61no—
159C2×C5×C8—61no—
160C2×C5×C8—61no—
161C2×C5×C8—61no—
162C2×C5×C8—61no—
163C42×C5—21no—
164C42×C5—21no—
165#685—24no—
166C4⋊Dic5—21no—
167C4⋊Dic5—32no—
168C4⋊Dic5—61no—
169C4⋊Dic5—61no—
170C4⋊Dic5—61no—
171C4⋊Dic5#6712yes—
172#683—122no—
173C2×C4×D4—51no—
174C2×#107—151no—
175C2×#102—151no—
176C2×#102—151no—
177#389—151no—
178#340—151no—
179#336—31no—
180C22×C3×C5C4×D411yescharacteristic
181C22×C3×C5#12011yescharacteristic
182C22×C3×C5C22⋊Q811yescharacteristic
183C22×C3×C5C2×D811yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C22×C3×C5#13711yescharacteristic
187C2×C3×D5—24no—
188C2×C3×D5—42no—
189C2×C3×D5—42no—
190C2×C3×D5—42no—
191C2×C3×D5—42no—
192C2×C3×D5—42no—
193C2×C3×D5—42no—
194C3×C4×C5—22no—
195C3×C4×C5—41no—
196C3×C4×C5C2×C4⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C22⋊Q811yescharacteristic
199C3×C4×C5#12311yescharacteristic
200Dic15—42no—
201Dic15—81no—
202C3×Dic5—42no—
203C24×C3—101no—
204C2×C3×D4—52no—
205C2×C3×D4—52no—
206C2×C3×D4—52no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C22×C3×C4—104no—
211C22×C3×C4—101no—
212C22×C3×C4—202no—
213C22×C3×C4—202no—
214C22×C3×C4D2011yescharacteristic
215C22×C3×C4D2011yescharacteristic
216C22×C3×C4C22×D511yescharacteristic
217C22×Dic3—101no—
218C22×Dic3—101no—
219C3×C4⋊C4—52no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—104no—
222C3×C42—21no—
223C3×C42—21no—
224C4⋊Dic3—52no—
225C4⋊Dic3—101no—
226C4⋊Dic3—101no—
227C4⋊Dic3—101no—
228Dic3⋊C4—202no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8C4×D512yescomplemented
235C23×C5C2×#6711yescharacteristic
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—41no—
240C22×D5—41no—
241C22×D5—41no—
242C22×D5—41no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5#21312yes—
249C2×C4×C5C2×Dic611yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5#23511yescharacteristic
253C2×C4×C5C2×#6711yescharacteristic
254C2×C4×C5C2×#6711yescharacteristic
255C2×Dic5—22no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—62no—
259C2×Dic5—121no—
260C2×Dic5—121no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C2×Dic5—121no—
264D20—22no—
265D20—22no—
266D20—22no—
267D20Dic3⋊C414yescomplemented
268C4×D5—48no—
269C5×C8—62no—
270C5×C8—121no—
271C22×D4—51no—
272C23×C4—101no—
273C22×C8—31no—
274C22×C8—31no—
275C4×D4—102no—
276C4×D4—102no—
277C2×C4⋊C4—51no—
278C2×C4⋊C4—151no—
279C2×C4⋊C4—151no—
280C2×C4⋊C4—301no—
281C2×C22⋊C4—101no—
282C2×C42D3×D511yescharacteristic
283#107—302no—
284#102—154no—
285#102—302no—
286#95—301no—
287C2×C3×C5#38511yescharacteristic
288C2×C3×C5C4×D811yescharacteristic
289C2×C3×C5#44011yescharacteristic
290C2×C3×C5#44711yescharacteristic
291C2×C3×C5#45211yescharacteristic
292C2×C3×C5#47411yescharacteristic
293C2×C3×C5#47811yescharacteristic
294C3×D5—44no—
295C23×C3—102no—
296C23×C3—102no—
297C23×C3—102no—
298C23×C3—201no—
299C23×C3—201no—
300C23×C3—201no—
301C23×C3—201no—
302C23×C3C2×D2011yescharacteristic
303C3×D4—54no—
304C3×D4—102no—
305C3×D4—102no—
306C3×D4—102no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—102no—
313C2×C3×C4—208no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4D4012yes—
317C2×C3×C4C2×C4×D511yescharacteristic
318C2×C3×C4#70911yescharacteristic
319C2×C3×C4D4×D511yescharacteristic
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4#71111yescharacteristic
322C2×C3×C4Q8×D511yescharacteristic
323C2×Dic3—102no—
324C2×Dic3—201no—
325C2×Dic3—201no—
326C2×Dic3—201no—
327C2×Dic3—201no—
328C2×Dic3—201no—
329C3⋊C8—22no—
330C3⋊C8—41no—
331C22×C5#92411yescharacteristic
332C22×C5C4×#6711yescharacteristic
333C22×C5C2×#21311yescharacteristic
334C22×C5#93211yescharacteristic
335C22×C5#95011yescharacteristic
336C22×C5#95111yescharacteristic
337C22×C5#95311yescharacteristic
338C2×D5—24no—
339C2×D5—42no—
340C2×D5—42no—
341C2×D5—42no—
342C2×D5—42no—
343C2×D5—42no—
344C2×D5—42no—
345C4×C5—22no—
346C4×C5—41no—
347C4×C5C2×Dic3⋊C411yescharacteristic
348C4×C5#92411yescharacteristic
349C4×C5C4×#6711yescharacteristic
350C4×C5#92911yescharacteristic
351Dic5—42no—
352Dic5—122no—
353Dic5—241no—
354C24—101no—
355C2×D4—52no—
356C2×D4—52no—
357C2×D4—52no—
358C2×D4—101no—
359C2×D4—101no—
360C2×D4—101no—
361C22×C4—104no—
362C22×C4—101no—
363C22×C4—202no—
364C22×C4—202no—
365C22×C4—301no—
366C22×C4—301no—
367C22×C4#120211yescharacteristic
368C22×C4#120211yescharacteristic
369C22×C4C2×D3×D511yescharacteristic
370C2×C8—32no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C4⋊C4—52no—
377C4⋊C4—101no—
378C4⋊C4—152no—
379C4⋊C4—301no—
380C4⋊C4—301no—
381C4⋊C4—301no—
382C4⋊C4—602no—
383C22⋊C4—104no—
384C42—21no—
385C42—21no—
386C3×C5#186211yescharacteristic, complemented, Hall
387C22×C3—104no—
388C22×C3—202no—
389C22×C3—202no—
390C22×C3—202no—
391C22×C3—202no—
392C22×C3—202no—
393C22×C3—202no—
394C22×C3C4×D2011yescharacteristic
395C22×C3#402811yescharacteristic
396C22×C3#404311yescharacteristic
397C22×C3C2×D4011yescharacteristic
398C22×C3#405011yescharacteristic
399C22×C3#405411yescharacteristic
400C22×C3#405511yescharacteristic
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—202no—
404C3×C4#402711yescharacteristic
405C3×C4#402911yescharacteristic
406C3×C4D5×C4⋊C411yescharacteristic
407C3×C4#404211yescharacteristic
408Dic3—202no—
409Dic3—401no—
410C2×C5#500711yescharacteristic
411C2×C5#500911yescharacteristic
412C2×C5C4×#21311yescharacteristic
413C2×C5#501811yescharacteristic
414C2×C5#521011yescharacteristic
415C2×C5#521711yescharacteristic
416C2×C5#523911yescharacteristic
417D5—44no—
418C23—102no—
419C23—102no—
420C23—102no—
421C23—201no—
422C23—201no—
423C23—201no—
424C23—201no—
425C23C2×#120211yescharacteristic
426D4—54no—
427D4—102no—
428D4—102no—
429D4—102no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—102no—
436C2×C4—208no—
437C2×C4—201no—
438C2×C4—201no—
439C2×C4—302no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4—601no—
443C2×C4—601no—
444C2×C4—601no—
445C2×C4#665312yes—
446C2×C4D5×Dic611yescharacteristic
447C2×C4#677111yescharacteristic
448C2×C4#677211yescharacteristic
449C2×C4C4×D3×D511yescharacteristic
450C2×C4D5×#6711yescharacteristic
451C2×C4D5×#6711yescharacteristic
452C8—62no—
453C8—121no—
454C2×C3—204no—
455C2×C3#6495711yescharacteristic
456C2×C3C4×D4011yescharacteristic
457C2×C3#6499911yescharacteristic
458C2×C3#6502111yescharacteristic
459C2×C3#6502211yescharacteristic
460C2×C3#6513511yescharacteristic
461C2×C3#6513611yescharacteristic
462C5#7160611yescharacteristic, complemented, Sylow
463C22—104no—
464C22—202no—
465C22—202no—
466C22—202no—
467C22—202no—
468C22—202no—
469C22—202no—
470C22C2×#665311yescharacteristic
471C22#9131111yescharacteristic
472C22#9131211yescharacteristic
473C22#9131311yescharacteristic
474C22#9136011yescharacteristic
475C22C4×#120211yescharacteristic
476C22#9156411yescharacteristic
477C4—22no—
478C4—41no—
479C4—202no—
480C4—602no—
481C4—1201no—
482C4#9134911yescharacteristic
483C4D5×Dic3⋊C411yescharacteristic
484C4#9144011yescharacteristic
485C4#9144711yescharacteristic
486C3#1059946311yescharacteristic, complemented, Sylow
487C2—204no—
488C2#1174688811yescharacteristic
489C2#1174688911yescharacteristic
490C2C4×#665311yescharacteristic
491C2#1174705211yescharacteristic
492C2#1174851211yescharacteristic
493C2#1174853111yescharacteristic
494C2#1174870411yescharacteristic
subgroupG/H
centerC23C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1862
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11751029C2semidirect
3. C2×#90990C2semidirect
6. C5×#4524C2semidirect
7. #11745980C2semidirect
24. #90965C4semidirect
54. C4⋊Dic15C2×C4semidirect
61. C2×C5×C3⋊C8C2×C4semidirect
71. #4524D5semidirect
121. C3×D20C4⋊C4semidirect
234. C2×C3⋊C8C4×D5semidirect
267. D20Dic3⋊C4semidirect
386. C3×C5#1862semidirect
462. C5#71606semidirect
486. C3#10599463semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×C4×D202
#117510292
C2×#909902
C2×#909652
C5×#45242
#117459802
#105994633
#716065